This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes:
at position (no holding stocks), long one short the other and short one long the other. A xed commission cost is charged with each transaction. We use a viscosity solutions approach to prove the existence and the explicit characterization of cut-off points via the resolution of quasi-algebraic equations. We illustrate our results by numerical simulations.